Fast isogeometric solvers for explicit dynamics

Handle URI:
http://hdl.handle.net/10754/563563
Title:
Fast isogeometric solvers for explicit dynamics
Authors:
Gao, Longfei; Calo, Victor M. ( 0000-0002-1805-4045 )
Abstract:
In finite element analysis, solving time-dependent partial differential equations with explicit time marching schemes requires repeatedly applying the inverse of the mass matrix. For mass matrices that can be expressed as tensor products of lower dimensional matrices, we present a direct method that has linear computational complexity, i.e., O(N), where N is the total number of degrees of freedom in the system. We refer to these matrices as separable matrices. For non-separable mass matrices, we present a preconditioned conjugate gradient method with carefully designed preconditioners as an alternative. We demonstrate that these preconditioners, which are easy to construct and cheap to apply (O(N)), can deliver significant convergence acceleration. The performances of these preconditioners are independent of the polynomial order (p independence) and mesh resolution (h independence) for maximum continuity B-splines, as verified by various numerical tests. © 2014 Elsevier B.V.
KAUST Department:
Applied Mathematics and Computational Science Program; Earth Science and Engineering Program; Numerical Porous Media SRI Center (NumPor); Physical Sciences and Engineering (PSE) Division; Environmental Science and Engineering Program
Publisher:
Elsevier BV
Journal:
Computer Methods in Applied Mechanics and Engineering
Issue Date:
Jun-2014
DOI:
10.1016/j.cma.2014.01.023
Type:
Article
ISSN:
00457825
Sponsors:
This work was supported in part by the King Abdullah University of Science and Technology (KAUST) Center for Numerical Porous Media and by an Academic Excellence Alliance program award from KAUST's Global Collaborative Research under the title "Seismic wave focusing for subsurface imaging and enhanced oil recovery".
Appears in Collections:
Articles; Environmental Science and Engineering Program; Applied Mathematics and Computational Science Program; Physical Sciences and Engineering (PSE) Division; Earth Science and Engineering Program

Full metadata record

DC FieldValue Language
dc.contributor.authorGao, Longfeien
dc.contributor.authorCalo, Victor M.en
dc.date.accessioned2015-08-03T11:54:33Zen
dc.date.available2015-08-03T11:54:33Zen
dc.date.issued2014-06en
dc.identifier.issn00457825en
dc.identifier.doi10.1016/j.cma.2014.01.023en
dc.identifier.urihttp://hdl.handle.net/10754/563563en
dc.description.abstractIn finite element analysis, solving time-dependent partial differential equations with explicit time marching schemes requires repeatedly applying the inverse of the mass matrix. For mass matrices that can be expressed as tensor products of lower dimensional matrices, we present a direct method that has linear computational complexity, i.e., O(N), where N is the total number of degrees of freedom in the system. We refer to these matrices as separable matrices. For non-separable mass matrices, we present a preconditioned conjugate gradient method with carefully designed preconditioners as an alternative. We demonstrate that these preconditioners, which are easy to construct and cheap to apply (O(N)), can deliver significant convergence acceleration. The performances of these preconditioners are independent of the polynomial order (p independence) and mesh resolution (h independence) for maximum continuity B-splines, as verified by various numerical tests. © 2014 Elsevier B.V.en
dc.description.sponsorshipThis work was supported in part by the King Abdullah University of Science and Technology (KAUST) Center for Numerical Porous Media and by an Academic Excellence Alliance program award from KAUST's Global Collaborative Research under the title "Seismic wave focusing for subsurface imaging and enhanced oil recovery".en
dc.publisherElsevier BVen
dc.subjectExplicit dynamicsen
dc.subjectFast isogeometric solversen
dc.subjectFinite element methoden
dc.subjectL2 projectionen
dc.subjectMass matrixen
dc.subjectTensor producten
dc.titleFast isogeometric solvers for explicit dynamicsen
dc.typeArticleen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentEarth Science and Engineering Programen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentEnvironmental Science and Engineering Programen
dc.identifier.journalComputer Methods in Applied Mechanics and Engineeringen
kaust.authorCalo, Victor M.en
kaust.authorGao, Longfeien
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